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Exam-Style Question on Significance

A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 436. This question is similar to one that appeared on an IB AI Standard paper (specimen) for 2021. The use of a calculator is allowed.

Ucayali, a multinational technology company that focuses on e-commerce, has a distribution centre in Camelot. As part of a study into healthy lifestyles, the number of cups of coffee drunk by 420 staff members each day were recorded. Results are shown in the table.

Cups of coffee per day

  none 1 or 2 3 or 4 5 or more
Office Staff 55 74 82 20
Warehouse Staff 21 33 49 21
Transport Staff 4 21 23 17

The company conducted a \(\chi^2\) test for independence at a \(5\%\) level of significance.

(a) State the null hypothesis.

(b) Calculate the p-value for this test.

(c) State, giving a reason, whether the null hypothesis should be accepted.

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